# projectiveFatPointsByIntersection -- computes ideal of fat points by intersecting powers of point ideals

## Synopsis

• Usage:
projectiveFatPointsByIntersection(M,mults,R)
• Inputs:
• M, , in which each column consists of the projective coordinates of a point
• mults, a list, in which each element determines the multiplicity of the corresponding point
• R, a ring, homogeneous coordinate ring of the projective space containing the points
• Outputs:
• a list, grobner basis for ideal of a finite set of fat points

## Description

This function computes the ideal of a finite set of fat points by intersecting powers of the ideals of each point.

 i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing i2 : M = transpose matrix{{1,0,0},{0,1,1}} o2 = | 1 0 | | 0 1 | | 0 1 | 3 2 o2 : Matrix ZZ <--- ZZ i3 : mults = {3,2} o3 = {3, 2} o3 : List i4 : projectiveFatPointsByIntersection(M,mults,R) 2 2 3 3 2 3 2 3 2 3 o4 = {y z - 2y*z + z , y - 3y*z + 2z , x*y*z - x*z , x z } o4 : List